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Chapter 3: Energy Bands Charge Carriers in Semiconductors

Ionic Bonding: ex) alkali halide (NaCl) Each Na (atomic

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Chapter 3: Energy Bands Charge Carriers in Semiconductors

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    1. Chapter 3: Energy Bands & Charge Carriers in Semiconductors

    2. Ionic Bonding: ex) alkali halide (NaCl) Each Na (atomic #=11; [Ne]3s1) atom gives up its outer 3s electron to a Cl atom, so that Na atom is made up of Na+ positive ions with electronic structure of Ne(1s22s22p6). Each Cl(atomic #=17; [Ne]3s23p5) atom receives an electron from a Na atom, so that Cl atom is made up of Cl- negative ions with electronic structure of Ar ([Ne]3s23p6) Coulomb forces exerted between a Na+ & 6 Cl- balanced with repulsive forces The ions have the closed-shell configurations of Ne and Ar ? no free electrons ? NaCl is a good insulator 1. Bonding Forces & Energy Bands in Solids

    3. 1. Bonding Forces & Energy Bands in Solids

    4. When 2 Si atoms are brought together: Linear combinations of atomic orbitals (LCAO) for two-electron wave functions (?1, ?2) of atoms leads to 2 distinct “normal” modes: a higher energy anti-bonding (anti-symmetric) orbital, and a lower energy bonding (symmetric) orbital (Pauli’s exclusion principle) For bonding state: an electron in the region between the two nuclei is attracted by two nuclei ? V(r) is lowered in this region ? electron probability density is higher in this region than for anti-bonding state ? It is the lowering of E of bonding state that causes cohesion of crystal 1. Bonding Forces & Energy Bands in Solids

    5. When N Si atoms (1s:2N, 2s:2N, 2p:6N, 3s:2N, 3p:2N electrons) are brought together to form a solid: As interatomic spacing decreases, the energy levels split into bands, beginning with valence (n=3) shell (sp3 hybridization) ? 3s & 3p bands grow and merge into a single band (8N states) ? As distance between atoms approaches the equilibrium interatomic spacing, this band splits into 2 bands separated by energy gap (Eg): upper band [conduction band; 4N states are empty(0K)], lower band [valence band; 4N states are completely filled with electrons (0K)].

    6. Insulator: Upper (conduction) band: empty (0K), lower (valence) band: completely filled with electrons (0K) Eg > 5 eV (much greater in insulator than in semiconductors) ? # of electrons excited from valence band to conduction band due to the increases of temperature and light intensity ? 0 ? current ? 0 because no charge transport can take place Semiconductor: Upper (conduction) band: empty (0K), lower (valence) band: completely filled with electrons (0K) Eg = 0.6-1.1 eV ? # of electrons excited from valence band to conduction band due to the increases of temperature and light intensity can be increased significantly ? current ? 0 because charge transport occurs

    7. E (energy) - k (propagation constant; wave vector) relationship: Free electron satisfies “k=<p>/h” For e- within a periodic lattice( has a periodic potential function) : energy gap Eg appears in E-k characteristics

    11. Intrinsic Semiconductor: a perfect semiconductor with no impurities or lattice defects VB is filled with electrons and CB is empty at 0K ? no charge carriers (insulator) EHP Creation (bond model): - If one of the Si valence electrons [gained enough E from higher T(=Eg; energy gap)] is broken away from its covalent bonds in the lattice such that it becomes free to move about in the lattice, a conduction electron is created and a broken bond (hole) is left behind. [valence electrons are excited thermally across Eg to CB (band model)]

    12. Doping: the process to create carriers in semiconductors by purposely introducing impurities into the crystal There are two types of doped semiconductors, n-type and p-type. Extrinsic semiconductors: the materials that have a characteristic of n0 ? p0 ? ni when they are doped n-type semiconductors: A “donor” impurity from column V (P, As, Sb; donor) introduces an donor energy level (Ed) near the bottom of CB Ec( within the band gap) At 50K, all of the electrons in Ed (filled with electrons at 0K) are “donated” to CB (e-: majority carrier, h+: minority carrier)

    13. p-type semiconductor (e-: minority carrier, h+:majority carrier): An “acceptor” impurity from column III (B, Al, Ga, In; acceptor) introduces an acceptor energy level (Ea) near the top of VB Ev( within the band gap) At 50K, all of the energy states in Ea (empty at 0K) “accept” electrons from the VB, leaving behind holes in the VB.

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